Journal of Productivity Analysis

, Volume 10, Issue 1, pp 7–20

A Quasi-Malmquist Productivity Index

  • E. Grifell-Tatjé
  • C. A. K. Lovell
  • J. T. Pastor

DOI: 10.1023/A:1018329930629

Cite this article as:
Grifell-Tatjé, E., Lovell, C.A.K. & Pastor, J.T. Journal of Productivity Analysis (1998) 10: 7. doi:10.1023/A:1018329930629


The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal distance function understates the distance to the relevant efficient subset, and the Malmquist productivity index is adversely affected, although in an analytically indeterminate direction. This has led us to consider a new definition of “one-sided” efficiency, and to develop a new nonradial efficiency measure which incorporates all slacks on the selected side. Replacing conventional radial efficiency measures with our new non-radial efficiency measures generates what we call a quasi-Malmquist productivity index. We illustrate our quasi-Malmquist productivity index with an application to productivity change in Spanish banking.

Distance FunctionsMalmquist Productivity IndexLinear Programming Slacks

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • E. Grifell-Tatjé
    • 1
  • C. A. K. Lovell
    • 2
  • J. T. Pastor
    • 3
  1. 1.Departament d'Economia de l'EmpresaUniversitat Autonoma de BarcelonaBellaterra (Barcelona)Spain
  2. 2.Department of EconomicsUniversity of GeorgiaAthensUSA
  3. 3.Departamento de Estadística e Investigacíon OperativaUniversidad de AlicanteAlicanteSpain